As an application of Theorem REF , we show that it implies that
Corvaja–Zannier's result on the geometric algebraic simple connectedness of normal proper varieties with the Hilbert property over number fields holds over finitely generated fields of characteristic zero. The proof of this extension is similar to Corvaja–Zannier's proof, except that we used a stronger version of the Chevalley–Weil theorem [1]} to prove Theorem REF . We will include the proof for the sake of completeness, and for illustrating the relevance of near-integral points.
